Analysis of Sub-Harmonic Resonance and Nonlinear Bifurcation Phenomena of Three-Dimensional Beams Under Parametric Excitation

Risers are one of the main vessel structural members. So, non-linear vibration analysis of risers, is particularly important. To achieve a proper design, understanding how the transverse vibrations of risers and obtain their frequency response is very useful. In this paper, the transverse vibrations analysis of risers under variable axial load are investigated. The effects of mid-plane stretching is also considered. For this study, the method of multiple time scale is used. In order to verify the accuracy of this method, the results are compared with the results of four order Runge-Kutta numerical method, which has a good accuracy. The frequency response of the system is represented Bifurcation phenomenon. Study of frequency response indicating that there is bifurcation phenomenon in vibrational system, and also the mid-plane stretching of riser will create a hardening behavior. Parametric study is also performed that the effect of various parameters is review on the starting point of the bifurcation phenomenon.